Numbers and Decimals

Movement of the Decimal Point

Adding and Subtracting Fractions and Decimals

Multiplying Decimals

Convert Fraction to Decimal Using Long Division

Convert Recurring Decimals to Fractions

Negative Numbers

Rational Numbers and their location on a Number Line

Adding and Subtracting Negative Numbers

Multiplying and Dividing Negative Numbers

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Convert Recurring Decimals to Fractions

Numbers and Decimals Convert Recurring Decimals to Fractions

Courses Overview

🎬 Video Tutorial

(0:01) How to Convert Recurring Decimals to Fractions: Start by setting the recurring decimal as ‘$x$’, then use multiplication to align the repeating parts, making subtraction possible to eliminate them.
(0:10) Turn One-Digit Recurring Decimal to Fraction (Example): Let $x = 0.333\ldots$; multiply by 10 to get $10x = 3.333\ldots$ Subtract the equations to find $9x = 3$. So $x = \large \frac{1}{3}$.
(0:46) Turn Two-Digit Recurring Decimal to Fraction (Example): Set $x = 0.4545\ldots$, multiply by 100 to get $100x = 45.4545\ldots$ Subtract the 2 equations to find $99x = 45$. So $x =\large \frac{5}{11}$.

📂 Revision Cards

Step-by-step guide converting 0.333 recurring decimal to fraction 1/3 by multiplying by 10, subtracting equations, and solving for x. — 1) Converting Recurring Decimals to Fractions

Converting the recurring decimal 0.4545... into a fraction, multiplying both sides by 100, subtracting the equations, and solving for x = 5/11. — 2) Converting Recurring Decimals to Fractions

Converting the recurring decimal 0.1666... into a fraction, showing multiplication by powers of 10, subtraction of equations, and solving to get 1/6. — 3) Converting Recurring Decimals to Fractions

🍪 Quiz Time - Practice Now!

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Convert Recurring Decimals to Fractions

1 / 6

Q: Convert $0.\overline{7}$ to a fraction.

$ \frac{7}{9} $

$ \frac{7}{11} $

$ \frac{7}{8} $

$ \frac{7}{10} $

Feedback: Not quite! Let $x = 0.\overline{7}$. Multiply both sides by 10: $10x = 7.\overline{7}$. Subtract $x = 0.\overline{7}$, leaving $9x = 7$. Solve for $x$: $x = \frac{7}{9}$.

Feedback: Well done! Let $x = 0.\overline{7}$. Multiply both sides by 10: $10x = 7.\overline{7}$. Subtract $x = 0.\overline{7}$, leaving $9x = 7$. Solve for $x$: $x = \frac{7}{9}$.

2 / 6

Q: Convert $0.\overline{12}$ to a fraction.

$ \frac{13}{99} $

$ \frac{6}{50} $

$ \frac{4}{25} $

$ \frac{4}{33} $

Feedback: Not quite! Let $x = 0.\overline{12}$. Multiply by 100 because the repeating part has two digits: $100x = 12.\overline{12}$. Subtract $x = 0.\overline{12}$, leaving $99x = 12$. Solve for $x$: $x = \frac{12}{99}$. Simplify the fraction: $x = \frac{4}{33}$.

Feedback: Well done! Let $x = 0.\overline{12}$. Multiply by 100 because the repeating part has two digits: $100x = 12.\overline{12}$. Subtract $x = 0.\overline{12}$, leaving $99x = 12$. Solve for $x$: $x = \frac{12}{99}$. Simplify the fraction: $x = \frac{4}{33}$.

3 / 6

Q: Convert $0.\overline{81}$ to a fraction.

$ \frac{9}{11} $

$ \frac{10}{22} $

$ \frac{27}{33} $

$ \frac{78}{99} $

Feedback: Not quite! Let $x = 0.\overline{81}$. Multiply both sides by 100 because the repeating part has two digits: $100x = 81.\overline{81}$. Subtract $x = 0.\overline{81}$, leaving $99x = 81$. Solve for $x$: $x = \frac{81}{99} = \frac{9}{11}$.

Feedback: Well done! Let $x = 0.\overline{81}$. Multiply both sides by 100 because the repeating part has two digits: $100x = 81.\overline{81}$. Subtract $x = 0.\overline{81}$, leaving $99x = 81$. Solve for $x$: $x = \frac{81}{99} = \frac{9}{11}$.

4 / 6

Q: Convert $0.1\overline{6}$ (0.1666 recurring) to a fraction.

$ \frac{1}{6} $

$ \frac{1}{9} $

$ \frac{1}{8} $

$ \frac{5}{30} $

Feedback: Not quite! Start with $x = 0.1\overline{6}$. Multiply by 10: $10x = 1.\overline{6}$. Then multiply by 100: $100x = 16.\overline{6}$. Subtract $10x = 1.\overline{6}$ to get $90x = 15$. Solve $x = \frac{15}{90} = \frac{1}{6}$.

Feedback: Well done! Start with $x = 0.1\overline{6}$. Multiply by 10: $10x = 1.\overline{6}$. Then multiply by 100: $100x = 16.\overline{6}$. Subtract $10x = 1.\overline{6}$ to get $90x = 15$. Solve $x = \frac{15}{90} = \frac{1}{6}$.

5 / 6

Q: Convert $0.\overline{123}$ to a fraction.

$ \frac{27}{297} $

$ \frac{123}{990} $

$ \frac{41}{333} $

$ \frac{123}{1000} $

Feedback: Not quite! Let $x = 0.\overline{123}$. Multiply by 1000 because the repeating part has three digits: $1000x = 123.\overline{123}$. Subtract $x = 0.\overline{123}$, leaving $999x = 123$. Solve for $x$: $x = \frac{123}{999}$. Simplify the fraction: $x = \frac{41}{333}$.

Feedback: Well done! Let $x = 0.\overline{123}$. Multiply by 1000 because the repeating part has three digits: $1000x = 123.\overline{123}$. Subtract $x = 0.\overline{123}$, leaving $999x = 123$. Solve for $x$: $x = \frac{123}{999}$. Simplify the fraction: $x = \frac{41}{333}$.

6 / 6

Q: Convert $0.2\overline{7}$ to a fraction.

$ \frac{27}{99} $

$ \frac{28}{99} $

$ \frac{5}{18} $

$ \frac{22}{90} $

Feedback: Not quite! Let $x = 0.2\overline{7}$. Multiply $x$ by 10: $10x = 2.\overline{7}$. Multiply the original equation by 100: $100x = 27.\overline{7}$. Subtract $10x = 2.\overline{7}$, leaving $90x = 25$. Solve for $x$: $x = \frac{25}{90} = \frac{5}{18}$.

Feedback: Well done! Let $x = 0.2\overline{7}$. Multiply $x$ by 10: $10x = 2.\overline{7}$. Multiply the original equation by 100: $100x = 27.\overline{7}$. Subtract $10x = 2.\overline{7}$, leaving $90x = 25$. Solve for $x$: $x = \frac{25}{90} = \frac{5}{18}$.

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